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DETERMINATION OF THE FUNDAMENTAL FREQUENCY OF TRANSVERSE VIBRATION OF RECTANGULAR PLATES WHEN THE THICKNESS VARIES IN A DISCONTINUOUS FASHION

The problem outlined in the title is solved, in an approximate fashion, for the situation where a discontinuous variation of the thickness takes place over a concentric, rectangular subdomain of the plate. Numerical values of the fundamental frequency coefficient are obtained for several combinations of clamped and simply supported edges and the governing geometric parameters. Two approaches have been used: a) the optimized Rayleigh-Ritz method employing polynomial coordinate functions, and b) the finite element method. An important practical conclusion of the investigation is the fact that dynamic stiffening of the plate is achieved for all the situations considered in the paper when the plate possesses a free, concentric, rectangular hole.